There are actually quite a few orchids that are pretty close to straight-up black. Not sure how many of these images the post will let me link, but here goes!
Catasetums can be very dark, some of the most famous being Fredclarkeara After Dark orchids which include some of the darkest blacks, and they have marvelous fragrance.
Dracula orchids have some pretty interesting color combos, Dracula vampira being probably the one with the most black.
There's a good number of black paphs, some almost totally black up through a whole range including varying amounts of other colors like red, purple, white or green on them.
Cymbidiums can come in very dark colors. Cymbidium Kiwi Baron 'New Horizon' is black with some pale pink in the middle.
Some Vandas can be quite dark, from very saturated purples to more blackish:
Maxillaria schunkeana is quite black, though it doesn't share the coconut fragrance of Maxillaria tenufolia, which is a dark red.
Encyclia cochleata is not too hard to find, and looks like weird little black-hooded octopi.
As for dark reds, there are lots of those!
Colmanara Masai Red
Cycnoches Wine Delight
Zygopetalums can come in nice dark color combinations, and tend to be fragrant.
And so on. Not all orchids are brightly colored, there are a lot that run an interesting range of browns, greens, purples, etc.